The technological progress function: a new technique for forecasting

OF THE

MASSACHUSETTS INSTITUTE
OF TECHNOLOGY

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Research Program on the
Management of Science and Technology

THE TECHNOLOGICAL PROGRESS FUNCTIONr
A NEW TECHNIQUE FOR FORECASTING-

Alan R. Fusfeld '

January 1970

#438-70

MASSACHUSETTS

INSTITUTE OF TECHNOLOGY

50 MEMORIAL DRIVE

CAMBRIDGE, MASSACHUSETTS 02139

Research Program on the
Management of Science and Technology

THE TECfiNOLOGlCAL PROGRESS FUNCTION?
A NEW TECHNIQUE FOR FORECASTING*

Alan R. Fusfeld "
January 1970 #438-70

-■=Based on a paper read at the annual meeting of TIMS in Atlanta,
October 3, 1969. This paper is being published in Technological
Forec asting , Volume 1, Issue 3, Winter 1970.

The author is a special student at MIT's Sloan School of Management,
E52-530, 50 Memorial Drive. Cambridge, Mass. 02139, while on
leave of absence from his senior year at The Johns Hopkins University,
Baltimore, Maryland.

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THE TECHNOLOGICAL PROGRESS FUNCTION:
A NEW TECHNIQUE FOR FORECASTING

1. BASIC ASSUMPTIONS :

The core of technological trend forecasting has most
often been based upon a plot of a technical parameter
against time. This study concerns the implications for
forecasting, when these technical parameters are plotted
against cumulative production.

For the examples covered in this study, the relation-
ships between technical characteristics and cumulative pro-
duction all have the mathematical form:

Ti = a(i)^ (1)

where Tj^ = value of parameter at the i^h unit,

i = cumulative production,
and a,b = constants.

This dependence of a technical value upon production is defined
here as the technological progress function . This paper relates
the development of that function, the implications of the math-

4.

ematical form just mentioned for trend forecasting, and
information compiled from a variety of case studies.*

It is of interest to note that the form of the technological
progress function is similar to that of the common industrial
"learning curve", as well as the learning curves of psychologists,
The industrial "learning curve" relates cost to production
(1, 2, 3) .

Yi - Yid)"^ (2)

where y- = cost of the i unit

i - cumulative production

st
y-^ = cost of 1 unit

b = constant .

and the psychological learning curve relates the efficiency

of performing a task to the number of repetitions (4, 5, 6, 7)

b

Ejj = k(N)

(3)

where

th

E„ = efficiency of performing N task
N = cumulative task number

k,b = constants

* Studies completed included:
civil aircraft-speed
military aircraft- speed
turbojet engines- specific weight
turbojet engines- specific fuel
consumption

automobiles- horsepower
electric lamps- lumens
computer programs- figure

of merit
hovercraft- figure of merit

5.

They are similar to the technological progress function,
T^ = a(i) , because all three show the measure of some
characteristic, for which improvement is desired, as an
exponential function of the cumulative number of repetitions
or production.

The environment in which technology develops is clearly
of additional interest and appears to affect the rate of
learning through discrete changes in the learning constant,
b. It must be specified here, that environment refers to
the external economic factors which surround the production
process. An example of this effect was the change in the
government investment and market potential relating to the
automotive industry in the late twenties (8, 9) , which
multiplied the rate of progress, b, by a factor of 6.2.

2. INTRODUCTION AND BACKGROUND INFORMATION :

The development of the technological progress function,
T^, characteristic of technological improvement, evolved
from a consideration of:

(1) problems and background factors inherent in

industrial progress relationships,

(2) indications from psychology that general phenomena

of "learning" were present,
and (3) difficulties in existing techniques of forecasting.

2.1 PROGRESS FUNCTIONS :

Briefly, industrial progress relationships are functions,
such as production costs/unit, maintenance costs/unit, and
manufacturing costs/unit, which can be written as a function
of costs associated with unit number one, the cumulative unit
number, and a learning constant. They are termed progress
functions because a reduction in costs indicates a gain in
efficiency. These functions, as previously mentioned, have
been found to have the precise form (1, 2, 10, 11):

yi - a(i)-b (1)

When plotted on log-log paper, this gives a straight line,
whose slope, -b, is the rate of progress, that is, the rate
at which efficiency is improving. It should be noted here

that, as previously mentioned, the technological progress
function has the same form and expression, the difference
being a positive rather than a negative slope.

Various studies of industrial progress functions have
shown that there are a number of causes or factors which
are common to most of the different types (1, 2, 11, 12, 13).
The more direct factors are:

1. engineering or desing improvements;

2. servicing technician progress;

3. job familiarization by workmen;

4. job familiarization by shop personnel and engineering
liason;

5. development of a more efficient parts upply system;
and 6. development of a more efficient method of manufacture.
The innate factors are:

1. the inherent susceptibility of an operation to improve-
ment ;
and 2. the degree to which this can be exploited.

These functions can be called "micro-economic progress
functions" (MEPF) because:

1. they are similar in mathematical form,
and 2. each relates to decisions of the "firm".
However, their applicability to development decisions is not

8.

as simple as it would seem initially since the functions
contain two areas of problems. Both areas are relevant
to the subject of the technological progress function be-
cause the first helped to prompt its development and the
second helps to explain its behavior.

The first area involves certain MEPF characteristics
which present problems of decision that have been unsolvable
because of their link with technological innovation. The
problems begin when one attempts to determine the component
costs of the first unit of production and finds that one must
arbitrarily set a limit upon the background development
expenses. A mechanism by which background and development
costs would be linked to all of the generations of a product
might help to alleviate this difficulty of first unit costs;
of course, this would first require a model for technological
change.

Further and more fundamental complications become apparent
when the development of new generations of equipment is con-
sidered, as opposed to the difficulties of measuring cost for
any one generation. Technical changes and design modifica-
tions are part of the inherent forces that cause the MEPF
to behave as it does, but there are no provisions for setting a
limit on these changes; the engineering change procedure of
firms being arbitrary in nature. That is to say that, after

a certain number of modifications in production procedure
or design, the product in reality will be a "new" product
and will be so labeled by sales and management. This is often
the case with developments resulting from both conscious and
unconscious defensive research, which is designed to improve
a product's competibility .

The locating of an "old-new" product line or determining
where a major change begins are questions posed by users of
the MEPF and seem to beg a progress function which cuts
across individual generation lines. The technological pro-
gress function is such a relationship and contains the same
factors of engineering learning and motivation of the MEPF,
which not only cause problems in its use but also provide a
major stimulus for technological advancement.

The other problem area relates to deviations from normal
(line a-rity on log-log paper) MEPF behavior. The explanations
of these differences are important, since they help to clarify
the effects of external factors of the environment on tech-
nological progress. Some of these deviations are due
to changes in the psychological motivation of the personnel
involved, as would be the case where a product line is sud-
denly scheduled for discontinuance or where the success of a
new development is announced to the employees (1, 2, 14).

10,

others would be due to changes in design or the introduc-
tion of new people to the job. Finally, if the product
or system is being constructed on parallel assembly lines
or shifts, the addition or subtraction of new lines, perhaps
with changes in demand, will cause anomalies in the MEPF
(14). All of these deviations cause a change in the
slope of the progress function. Thus, it is implied
that changes in the rate of progress (i.e., the slope of
the progress function) are not random but are a function
of critical parameters forming part of the external environ-
ment.
2.2 PSYCHOLOGY :

In addition to the information supplied by analysis of
progress functions, further insight has been gained from
psychological learning theory. Since there is considerable
dispute over exact definitions of what learning is or is not,
let me point out that, here, psychological learning refers to
perceptible gains in performing given tasks. These tasks in
academic studies have ranged from solving puzzles and going
through mazes to simple studies of response time for given
stimuli. It has been noted in a variety of projects concerning
both animals and people, that the efficiency of performing a

11.

given tasks increases with the cumulative number of repeti-
tions (4, 5, 7, 14, 15, 16). It should also be pointed out
that none of the studies differentiate between the fre-
quency of the repetitions as long as the frequency was within
the maximum retention interval. The studies found that,

Ejj = K(N)^ (2)

where Ejj = efficiency in performing the N^^ task,

N - the cumulative task number,
and K, a = constants.

Such a relation was particularly apparent in a 1934 study
with children by Melcher (7) and in a 1955 study with dogs
by Bush and Hosteller (4) . A similar but different relation-
ship regarding repetitious activity can be derived from work
presented by Frank Logan in his book. Incentive (16). Logan
noticed of his subjects, that they, "...behave in such a way
as to maximize reward while at the same time minimizing effort."
Such behavior is not only identical with the aims of man's
economic endeavors, but is also a causal factor of technological
progress . Since the progress functions discussed previously show
a similar dependency on repetition of tasks, it would appear
that the same type of learning discussed above is involved.
2. 3 FORECASTING :

The third area that has contributed to the present develop-
ment of the technological progress function is technological

12,

forecasting. The primary methods already available, such
as Delphi, trend extrapolation, trend correlation, and
growth analogy, do not allow for the easy or precise handl-
ing of environmental factors (17), This provided further
incentive to find a progress function that would be a6 com-
petent as other techniques under constant forces and yet
allow for environmental change.

13.

3. TECHNIQUES USED IN ANALYSIS;

The work involved in investigating and defining the techno-
logical progress function was completed through two separate
lines of reasoning. Both paths were developed while taking
note of:

(1) an observation, through analysis of the MEPF, that
the independent variable should be the cumulative production
number;

(2) an implication in learning theory that the form of the function
should be similar to that of the MEPF and the general structure
characteristic of improvement functions; and

(3) a need of forecasting techniques for a term through which
environmental change could be introduced.

The paths chosen for development are common to most scientific
endeavors. They were those of theoretical derivation from known
relationships and empirical model building from real world data.

14.

The theoretical side bases itself on the eauivalence, for
at least certain areas, of the rate of patent output with
technological /growth or prc^-ress. Through relationships
derived or shown by Schmookler (l8) and Villers (19), the
rate of patent output was related to investment and expected
profit functions. Prom this point, substitutions were made
from investment/profit functions, denoting technical ad-
vance.

The result was a rela.tionship that equated the level of
technological improvement to a constant multiplied by an
increasing Quantity dependent function raised to a positive
exponent , i.e.,

T. = K( f(i) )^ (3)

th
where T. = the level of technology at the i unit of

production,

f(i) « a function which varies with the production

number, i,

and K,c = constants.

15.

Although it seemed to substantiate earlier hypotheses, it
could only be taken as a further indication that this might
be the correct approach, since it was not precise enough in
nature to stand by itself.

The results of the theoretical derivation cleared away
doubts from the proposed directions of the empirical phase
of the study. At this stage, it was clear that the work
should attempt to correlate technological improvement with
the cumulative quantity of production. In addition, thoughts
of incorporating the results with other progress functions
motivated the gathering of data designed for more extensive
correlations.

Real data were then sought to provide information on tech-
nical parameters, production, and costs with background infor-
mation to be provided where possible. One could then observe
the behavior of technological parameters with respect to pro-
duction under the sets of conditions forming the background
environment.

However, before describing the case studies and conclusions
some of the difficulties involved in this work should be pointed
out. The most difficult problem was that of obtaining accurate
data, particularly with regard to cost information. This was

16.

solved by combining data from several sources and v/here
possible having the material validated by someone fa .iliar
with the field.

Other nroblems arose concerning the choice of tech-
nical parameters. In this care decisions were made from
background information and observation of changes in the
parameter with resoect to cost changes.
4. F.IJSENTATION OF DATA;

The empirical studies discussed here verified both the
preliminary hyootheses and the theoretical derivation and
were based upon ana.lyses of data regarding the aircraft
industry, the electric lamp industry, and computer pror^rammmin" .
4.1 AIRCRAFT DATA :

The data from the aircraft industry concerned turbo-jet
engine development over a period of nearly twenty years and
was synthesized from two Air Force Institute masters theses
(20,21), sup'oorting information supplied by the Pratt &
Whitnoy Division of United Aircraft (22), and Aviation I'acts
and Figures 1958 (23). From these sources, production cost/
unit, production by year, ciAmulative production, and trie tech-
nological parameters were observed.

The results have shown, in Figure 1, that technological
progress, as represented by s-ecific weignt ( dry engine weiglit/

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Figure 1

TURBO-JET ENGINE CHARACTERISTICS

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pounds of thrust) and specific fuel consumption (pounds of
fuel/hr ./pound of thrust) is log- linear to a logarithmic
quantity axis, where quantity indicates the cumulative pro-
duction of engines within the turbo-jet family. It also
appears that an arithmetic time axis may be used in place of
a logarithmic quantity axis on many occasions for the same
accuracy, whenever production undergoes constant percentage
increases with respect to time*,
4.2 ELECTRIC LAMP DATA ;

The Electric lamp industry data was obtained by combing
information from James Bright ' s book Automation and Manage -
ment , (24) and Arthur A. Bright ' s book. The Electric Lamp
Industry , (25) for 60 watt lamps. These sources enabled the
study to be concerned with technological progress as re-
presented by the output of the lamp in lumens, production
by year, and cumulative production. The many development
changes made it unnecessary to examine each individual generation
of lamp.

The results confirm the existence of a technological
progress function behaving in accordance with the generalized
MEPF principles. Figure 2, where this is illustrated, actually

* The bracketed points at the end of the "specific weight" curve were
obtained from current advertising information of Pratt & Whitney
presented in Aviation Week during March, 1969.

pif^ure 2

ELECTRIC LMP LUMEN OUTPUT

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indicates the existence of two rates of progress. One ex-
tends from 1912 until 1920 and the second from 1920 until
1940. This would imply that the external environment
affecting the lamp industry underwent a shift. Since the
production which had been increasing at a steady 9.39% per
year throughout the first period concurrently suddenly
shifted downward to a rate of 2.74% growth at the same tran-
sition point (Figure 3), it may be concluded that one or
more changes in the environment increased the value of the
exponent "b" in the technological progress equation, while
at the same time decreasing the rate of growth of production.

fUe

It IS interesting to note comparison between the progress
function for lamps as shown in Figure 2 with the more usual
forecasting method shown in Figure 4. This data substantiates
a possible claim that forecasting results with an arithmetic
time axis are as good as they have been because of the substi-
tution effect. That is, an arithmetic time axis may be sub-
stituted for a logarithmic quantity axis, when production
quantities increase in reasonably constant percentages with
time, as in Figure 3.
4.3 COMPUTER PROGRAMMING DA TA:

An additional example has been drawn from a specific
experience in programming. Data for this example was made

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ELECTRIC LAMP PRODUCTION VS TllIB

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available through the help of John Cleckner, a student at The

Johns Hopkins University. The example represents the rate of

progress in the development of a single computer program

developed solely by him under special arrangement with an area

firm. A figure of merit was determined which would best represent his ow

aims while developing the program. This figure of merit equals the

lines of output divided by the running time. The computer pro=

gram dealt with an estimation of bakery goods to be sold according

to the day of the week, store, and particular item.

In an analogy to the development of products, it was
decided to regard the last best figure of merit (Figure 5) for a
particular run as the figure of merit to be processed. T|iis may
or may not be the true figure of merit for that run, but it
would be an accurate representation of the figure of merit of the
best program available at any given point in its total development.

The results illustrate several areas of interest. The
first is the applicability of the technological progress function
to the area of programming. There is also the observance of
different slopes corresponding to different development phases.
Finally, since the work was done by one person, the analysis indicates
the possible role of psychological "learning" theory in techno-
logical progress.
ADDITIONAL EXAMPLES:

Other cases studied demonstrated similar technological

A COMPUTER PROGRAM DEVELOPMENT

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20,

progress functions, that is, linearity on log-log paper
when the technical progress parameter is plotted against pro-
duction. Those cases not discussed here are civil aircraft-
speed, military aircraft-speed, automobile -horsepower ,
hovercraft-figure of merit, and an office machine development-
figure of merit.

One could get the impression, from the data just discussed,
that the trends observed were basically limited to items of
hardware, but this was not found to be the case, as evidenced
by studies of the totally different area of agricultural
efficiency. From information pertaining to the pounds of rice
produced per acre in Japan over a period of twelve hundred years,
three log linear trends were noticeable (26,27). The two major
lines were a "long term" or ancient trend line and a modern
trend line of much steeper slope. By calculating backwards,
it was found that they intersected at a period of great external
change-- the "opening of Japan". The third line was a moderate
decrease in slope, which prevailed during the period of World
War II.

21,

THE TECHNOLOGICAL PROGRESS FUNCTION :

Thus, if we assume that Initial studies are correct ,
technological progress functions exist and are of the same
general nature as other micro-economic progress functions .
It is then further implied, that technological progress, as
denoted by a positively increasing function is logarithmically
linear with respect to a logarithmic quantity axis under con-
stant external forces. Over periods of time during which
external forces vary, the slope of the line, that is, the rate
of progress, may undergo discrete shifts. Such a function is
denoted as,

T. = a(i)^, (4)

1

where T^ = the value of the technological parameter,
i = the cumulative production number,
a = a constant associated with unit number one,

and b = the rate of progress, a variable, which is a function
of the external environment.

22

5.1 MATHEMATICS :

A brief glance at the mathematics shows that where b is

a constant:

log (Tj_) = b log (i) + log (a) (5)

and regarding the differential of (5)

dT-L = b di

T^ i (6)

Equation (6) indicates that, b, being constant, the percent-
age change in a technical parameter is a linear function of
the percentage change in cumulative production.
In addition, it should be noted that:
if i = (constant) e , (7)

log (i) = Kt + log (constant) (8)

and di = Kdt . (9)

i

Equation (9) represents a percentage change in production as

a linear function of time, that is, what has been referred to

as a "substitution effect".

Where di = Kdt,
i

d T^ = bKdt, (10)

which is the traditional trend forecasting relationship (28) .

5.2 RATE OF PROGRESS ;

From analysis of background information involved in the
work discussed above and current studies, the rate of pro-

grass, b, has been designated as a function of:

L/ the effective sii:e of the technical labor force;
o(, an intelligence factor-average educational level;
n, , a pre-learning factor-average experience level;
I, the level of investraent;

I, the rate of change of the level of investment;
d, a r.\aturation factor-durability of item-corripatability;
na, the anticipated raue of change of raarket derriand-slope
of sales curve;
and c, tha corrjTiunica'cion or diffusion rate.
Currently, work is being done to define the exact nature of
the function just described within the inherent constraints
that b is greater than, or equal to, 7ero and never infinity and
that if L,c^, 6, I, or m go to ^ero, then b also goes to ?ero
6. SUMMARY :

This study has been concerned with the technological pro-
gress function. The study proposes that the technological pro-
gress function may be based on the cumulative production unit
number on a logarithmic scale, as opposed to the arithmetic time
series base used for most forecasts. In this form, the techno—-
logical progress function allows for environmental changes to
act upon the rate of progress in a precise manner, that is, dis-
crete changes in the slope of the function. However, it should
be noted, that no less care must be taken when employing this

24,

technique in addition to or instead of existing methods,
particularly with regard to physical constraints imposed
upon the system.
7. FUTURE WORK -

The technological progress function is a tool to be used
with other techniques by the foresighted corporate and military
development planner, who can no longer overlook the effect of
technological change upon his proposals for future development.
Although, it is doubtful that a true "Newton's Law" for pre-
dicting technological advancement will ever be made, it is
believed that the development of the technological progress
function is a step towards more effective predictive methods.

Considerable work remains to be done in exploring the
nature and anomalies of the technological progress function
itself. There is, of course, the need for a precise definition
of the rate of progress function. In addition, there are
avenues of research concerning macro-economic implications
and ways in which the function might be of maximum value to
technologically oriented firms.

25.

REFERENCES

(1) H. Asher, Cost-Quantity Relationships in the Airframe

Industry . Project Rand-291, July, 1956.

(2) W, B. Hirschmann, "Profit Prom the Learning Curve",

Harvard Business Review , Jan-Feb, 1964.

(3) J. L. Kottler, "The Learning Curve- A Case History In

Its Application", The Journal of Industrial Engineers ,
AIIE, July-Aug, 1964.

(4) R. R. Bush, F. Llosteller, Stochastic Models of Learning ,

John V/iley and Sons, Inc., New York, 1955.

(5) J. Deese, Psychology of Learning , McGraw-Hill, New York,

New York, 1967.

(6) C. I. Hovland, I. L. Javis, H. H. Kelley, Communication and

Persuasion , Yale University Press, New Haven, Conn.,

1953.

(7) H. T. Melcher, Children's Motor Learning Vv'ith and V/ithout

Vision , The Johns Hopkins University Ph.D. Dissertations,

1934, p. 333.

(8) W. Owen, Automotive Transportation , The Brookings Institutim,

Washington, D.C., 1949.

(9) F. Stuart, ed.. Factors Affecting Determination of Market

Shares in the American Auromobile Industry , Hofstra
University Yearbook of Business, Series 2, vol. 3,
New York, October, 1965.

26.

(10) J. G. Abramowitz, G. A. Shattuck, Jr., "The Learning Curve",

IBM Report No. 31.101, 1966.

(11) J. G. Kneip, "The Maintenance Progress Function", The

Journal of Industrial Engineers , AIIE, Nov-Dec, 1965.

(12) R. A. Conway, A. Schultz, "The Manufacturing Progress Function",

The Journal of Industrial Engineers , AIIE, Jan-5'eb, 1959*

(13) M. E. Salveson, "Long Range Planning in Technical Industries",

The Journal of Industrial Engineers , AIIE, Sept-Oct, 1959.

(14) J. H. Russell, "Predicting Progress Function Deviations",

IBM Teclinical Report TR 22.446, August 28, 1967.

(15) C. L. Hull, C. I. Hovland, R.T. Ross, M. Hall, D. T. Perkir^

F. B. Fitch, Mathematico-Deductive Theory of Rote Learn-
ing , Yale University Press, New Haven, Conn., 1940.

(16) F. A. Logan, Incentive , Yale University Press, New Haven,

Conn., I960.

(17) M. J. Cetron, "Forecasting Technology", Science and Technology ,

Sept, 1967.

(18) J. Schmookler, Invention and Economic Growth , Harvard

University Press, Cambridge, Mass., 1966.

(19) R. Villers, Research and Development; Planning and Control ,

Rautenstrauch and Villers, New York, New York, 1964.

(20) R. E. Burckhardt, Major USAF, ''Cost Estimating Relationships

for Turbo-jet Engines", masters thesis, GSM/SM/65-3,
December, IS 65.

27.

(21) R. P. Gould, Major USAP, "Turbo-jet Engine Procurement Cost
Estimating Relationships" , masters thesis, GSM/SM/65-10,
August, IS 65.

(2?) N. Turkowitz, letter to author, November 5, 1968.

(23) Aviation Facts and Figures- 19^8 > American Aviation Publicatit-n

1958.

(24) J. R. Bright, Automation and Management , Harvard University,

Boston, Mass., 1958.

(25) A. Bright, The Electric Lamp Industry , McGraw-Hill, Nev/ York,

1949.

(26) H. Kahn, A. J. Wiener, The Year 2000 , The MacMillan Co.,

New York, 1967.

(27) W. W. Lockwood, The Economic Development of Japan , Princeton

University Press, Princeton, New Jersey, 1954.

(28) R. C. Lenz, Jr., "Technological Forecasting, Air Force

Systems Command, Wright Patterson Air Force Base,
Ohio, AD 408 085, ASD*TDR^62-414, June, 1962.

28.
BIBLIOGRAPHY

BOOKS

Almon, C. Jr., The American Economy to 1973 > Harper and Row,

New York, 1966.
Automation and Technological Change , The American Assembly at

Columbia University, Prentice-Hall, Enrlewood Cliffs,

New Jersey, 1962.
Ayres, K., Technological Forecasting and Long Range Planninf- ,

McGraw-Hill, New York, 1969.
Bright, J. R., Research, Development and Technological Innovation ,

Richard D. Irwin, Homewood, 111., 1964.
Bright, J. R., (ed.) Technological Forecasting for Industry and

Government , Prentice-Hall Inc., Englewood Cliffs, New

Jersey, 1968,
Brown, M. On the Theory and Measurement of Technological Change ,

Cambridge University Press, Cambridge, England, 1966.
Cetron, W. J., Technological Forecasting - A Practical Approach ,

Gordon and Breach, New York, 1969.
Hitch, C. J., Roland N. Mokean, The Economics of Defense in the

Nuclear Age , Harvard University Press, Cambrid;':e, Mass., 1967
Human Relations in Industrial Research Management, (ed) .^obert

Teviot Livingston, Stanley H. Milberg, Columbia University

Press, New York, 1957.

29.

Ma.nsfield, E., The Economics of Technological Change , W. W.

I

Norton and Co., New York, 1968.

Mansfield, E., Industrial Research and Technological Innovation ,

W. W. Norton and Co., New York, 1568.
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Schon, D. A., Technology and Change , Delacorte Press, New York,

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Warner, Columbia University Press, New York, 1966.

30.

ARTICLES

Bright, J. R., "Can We Forecast Technology?", Industrial
Research , March 5, 1968.

Cetron, M. J. ,R.J. Happel, W.C. Hodgson, W.A. McKenney, T.I. Monahan,
"A Proposal for a Navy Technological Forecast", Naval
Material Command, Washington, D.C.
Part I- Summary Report AD 65919 9
Part II- Back Up .{eport AD 659 200 May 1, 1966.

Cetron, M. J., A. L. V/eiser, "Technological Change, Technological
Forecasting, and Planning R&D, A View Prom the R&D
Manager's Desk", The George Washington University Law
Review , Vol. 36, No. 5, July, 1968.

Darracott, H.T., M.J. Cetron et al, "Report on Technological Fore-
casting", Joint Army Material Comrn and/Naval Material
Command/ Air Force Systems Command, Washington, D.C,
AD 664 165, June 30, 1967.

Duranton, R. A., "Quelques Remaroues Sur Les Courbes D ' Accoutumance" ,
Internal IBM Report, May 13, 1965.

Mahanti, B., "Progress Report/Manufacturing Progress Function

Report", Internal IBM paper (German Office), April 9, 1964.

"The Growth Force That Can't Be Cverlooked", Business Week ,
McGraw-Hill, New York, August 6, I960.

31^

"The Dynamics of Automobile Demand", General Motors Corp.,

New York, 1939.
Technology and World Trade , US Department of Commerce, NBS Misc.

Pub. 284, (symposium — 11/16, 17/66) .

ACKNOWLEDGEMENTS

The author offers special thanks to John Cleckner, Class of 1970,
The Johns Hopkins University, for his suggestions and help in prepar-
ing the data on computer programming. The author is also indebted
to Lisa Geiser, Class of 1972, Goucher College and Nancy Smith,
Class of 1972, Goucher College for their help in developing additional
data. In addition, Norman Turkowitz of Pratt and Whitney must be
noted for supplying the supporting information for the aircraft
engine study, for which the author is also very grateful.

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